Problem 45257. Find neighbor triangle indices

Created by Nicolas Douillet

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{"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","targetMode":"","relationshipId":"rId1","target":"/matlab/document.xml"},{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/output","targetMode":"","relationshipId":"rId2","target":"/matlab/output.xml"}],"parts":[{"partUri":"/matlab/document.xml","relationship":[],"contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n<w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>First input T is a triangulation (triplet list of indices -positive integers-, each index refering to a vertex number in a corresponding vertices list).</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Given a second input t (a certain triangle row index), one would like to query the list L of all its triangle neighbor indices.</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>A triangle is neighbor to another triangle if they share exactly one edge.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>For instance if</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[T = [1 2 4;...\n 2 3 4;...\n 5 6 8;...\n 6 7 8;...\n 1 2 5;...\n 2 5 6;...\n 2 3 6;...\n 3 6 7;...\n 3 4 7;...\n 4 7 8;...\n 4 1 8;...\n 1 8 5]]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>and t = 3, then the function should return</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[L = [4, 6, 12]']]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>since rows / (triangles of T) 4, 6, and 12 contain an edge in common with triangle / row 3.edge [6 8] for the first, edge [5 6] for the second, and edge [8 5] for the third.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Hypothesis :</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>- Since a triangle is not considered neighbor of itself,</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>t should not be part of L.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>- Order doesn't matter, but</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>T must be a column vector containing all the neighbor</w:t></w:r><w:r><w:t> triangle -row- indices (except itself then) once only.</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>No duplicata is admitted.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>-</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t>Edges are symmetric : [e1, e2] is the same edge as [e2, e1]</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>- Every indices are positive, distinct integers.</w:t></w:r></w:p></w:body></w:document>"},{"partUri":"/matlab/output.xml","contentType":"text/xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\" ?><embeddedOutputs><metaData><evaluationState>manual</evaluationState><layoutState>code</layoutState><outputStatus>ready</outputStatus></metaData><outputArray type=\"array\"/><regionArray type=\"array\"/></embeddedOutputs>"}]}

First input T is a triangulation (triplet list of indices -positive integers-, each index refering to a vertex number in a corresponding vertices list).Given a second input t (a certain triangle row index), one would like to query the list L of all its triangle neighbor indices. A triangle is neighbor to another triangle if they share exactly one edge.For instance if<pre class="language-matlab">T = [1 2 4;...
 2 3 4;...
 5 6 8;...
 6 7 8;...
 1 2 5;...
 2 5 6;...
 2 3 6;...
 3 6 7;...
 3 4 7;...
 4 7 8;...
 4 1 8;...
 1 8 5]
</pre>and t = 3, then the function should return<pre class="language-matlab">L = [4, 6, 12]'
</pre>since rows / (triangles of T) 4, 6, and 12 contain an edge in common with triangle / row 3.edge [6 8] for the first, edge [5 6] for the second, and edge [8 5] for the third.Hypothesis :- Since a triangle is not considered neighbor of itself, t should not be part of L.- Order doesn't matter, but T must be a column vector containing all the neighbor triangle -row- indices (except itself then) once only. No duplicata is admitted.- Edges are symmetric : [e1, e2] is the same edge as [e2, e1]- Every indices are positive, distinct integers.

First input T is a triangulation (triplet list of indices -positive integers-, each index refering to a vertex number in a corresponding vertices list).

Given a second input t (a certain triangle row index), one would like to query the list L of all its triangle neighbor indices. *A triangle is neighbor to another triangle if they share exactly one edge.*

For instance if

T = [1 2 4;...
       2 3 4;...
       5 6 8;...
       6 7 8;...
       1 2 5;...
       2 5 6;...
       2 3 6;...
       3 6 7;...
       3 4 7;...
       4 7 8;...
       4 1 8;...
       1 8 5]

and t = 3, then the function should return

L = [4, 6, 12]'

since rows / (triangles of T) 4, 6, and 12 contain an edge in common with triangle / row 3.edge [6 8] for the first, edge [5 6] for the second, and edge [8 5] for the third.

Hypothesis :

- Since a triangle is not considered neighbor of itself, *t should not be part of L.*

- Order doesn't matter, but *T must be a column vector containing all the neighbor* triangle -row- indices (except itself then) once only. *No duplicata is admitted.*

- *Edges are symmetric : [e1, e2] is the same edge as [e2, e1]*

- Every indices are positive, distinct integers.

Solve

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Last Solution submitted on Apr 11, 2023

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Problem 45257. Find neighbor triangle indices

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